WASHINGTON (CNN) -- As partisans argued pointedly over same-sex marriage outside the U.S. Supreme Court building, either hoping for or dreading a landmark decision, justices inside seemed reluctant Tuesday to extend a sweeping constitutional right for gays and lesbians to wed in all 50 states.

In the first of two days of hearings on cases that have the potential to fundamentally alter how American law treats marriage, Justice Anthony Kennedy -- considered the likely deciding vote on the divided court -- questioned whether justices should even be hearing the issue.

"This was a deeply divided Supreme Court, and a court that seemed almost to be groping for an answer here," said CNN Senior Legal Analyst Jeffrey Toobin, who watched the arguments.

On the point of allowing same-sex marriage in California, Justice Elena Kagan, a liberal member of the court, asked, "What harm is there to the institution of marriage?"

But more conservative members of the court took a go-slow approach. Justice Samuel Alito said the law on same-sex marriage is too new.

"There isn't a lot of data on its effect" on children and the institution of marriage, he said.

Attorneys who represented the two couples seeking to overturn California's Proposition 8 ban on same-sex marriages said they couldn't tell how the court would rule.

"We are confident where the American people are going with this," said Theodore Olson. "We don't know for sure what the United States Supreme Court is going to do, but we're very, very grateful they listened, they heard, they asked hard questions, and there's no denying where the right is."

On Wednesday, the court will listen to arguments in a separate case over the federal Defense of Marriage Act, a 1996 law that defines marriage as between a man and a woman.

While the court heard 80 minutes of arguments, supporters of same-sex marriage rallied outside the Supreme Court, hoping justices would reach for a broad ruling that would strike down bans nationwide.

"We are not asking for anything more than our neighbors, friends and family, but certainly expect no less," said Todd Bluntworth, who spoke with his husband and their two children to a crowd of supporters hoping for a historic ruling from the Supreme Court striking down laws banning same-sex marriage.

But opponents who rallied nearby urged the court to keep out of the issue and leave the decision to states.

"If you want to get married, go to one of the states that allows gay marriage," said Carl Boyd Jr., a conservative Nashville talk-show host. "Stop trying to force your agenda down our throats. Quit trying to bully the American people with the homosexual agenda."

Some demonstrators carried sign reading "Kids do best with a mom & dad."

Tuesday's hearing involved Proposition 8. Voters approved the proposal 52% to 48% in November 2008, less than six months after the state Supreme Court ruled that marriage is a fundamental right that must be extended to same-sex couples.

The overriding legal question is whether the 14th Amendment guarantee of equal protection under the law prevents states from defining marriage as California has.

Two of the key plaintiffs are Paul Katami and Jeff Zarrillo, a Burbank, California, couple who want to marry but can't because of Proposition 8. They say the state is discriminating against them for their sexuality.

"Stigma is stigma. And discrimination is discrimination," Katami told CNN.

"I think that any time there's discrimination in the country, it needs to be addressed and it needs to be taken care of," he said. "And that's why we feel that anytime in our history when there's been racial discrimination or sexual discrimination of orientation, or in particular marriage at this point, that we always bend toward the arch of equality."

Patchwork state laws

If the court decides in their favor, it would mark a historic shift in how the law treats marriage, striking down laws across the country banning same-sex marriage and matching an apparent cultural shift toward acceptance of same-sex couples.

Or the court could leave the current patchwork of state laws in place, choosing to let state legislatures and state courts sort it all out.

Forty-one states now forbid same-sex marriage, although nine of them allow civil partnerships. Nine other states allow same-sex marriage, and about 120,000 same-sex couples have gotten married, according to estimates.

California's bans seem to run counter to polls that show rising support overall for same-sex marriage. A CNN/ORC International poll released Monday found that 53% of Americans now support same-sex marriage, up from 40% in 2007.

The Supreme Court has ruled more than a dozen times that marriage is a fundamental right, "and as it relates to a fundamental right, the court will hold that under the highest level of scrutiny," Harris said.

The Defense of Marriage Act bars the federal government from recognizing state-sanctioned same-sex marriages. It prevents legally married gay and lesbian couples from getting federal benefits and privileges, like tax breaks and survivor benefits, that are extended to opposite-sex married couples.

No immediate decision

The court is unlikely to announce its decision until June.

But people could get a sense of which way the decision will go by listening to the questions posed by Kennedy, said Toobin, the legal analyst.

The court's four liberal justices are likely to vote to overrule Proposition 8, he said. Four conservatives are likely to vote to keep it.

"The most likely person to give the fifth vote is Anthony Kennedy," who previously authored two important gay rights decisions, Toobin said.

Partisans speak out

Same-sex marriage supporters say it's time for the court to take a stand that puts all Americans on the same footing.

"This is about our equality," Katami said. "This is about our freedom and our liberty. So we are not trying to topple marriage. We are not trying to redefine marriage. What we are trying to say is that equality is the backbone of our country."

But supporters of Proposition 8 and DOMA say the Supreme Court should stay out of the issue and let voters decide what they want.

"Our most fundamental right in this country is the right to vote and the right to participate in the political process," said Austin Nimocks of the Alliance Defending Freedom, a Christian advocacy group.

"We don't need the Supreme Court to take that right away from Americans of good faith on both sides of this issue and impose its judicial solution," Nimocks said. "We need to leave this debate to the democratic process, which is working."

Political positions

The Obama administration has formally expressed support for same-sex marriage in California, weighing in on the case in a brief last month. Obama, whose views on the issue have changed over his political career to full support, said he would vote to strike down the state's law if he sat on the court.

In what some have labeled the "nine-state strategy," the Justice Department argument is expected to center on the idea that civil union and domestic partnership laws may themselves be unconstitutional and that those states should go all the way and grant same-sex couples full marriage rights.

Other prominent politicians have expressed timely opinions in recent weeks, indicating the importance of the matter in the social context of 21st century American politics.

Hillary Clinton, the former secretary of state and possible 2016 Democratic presidential candidate, recorded a video for a gay rights group indicating her support.

Republicans have described cracks appearing in their party's long-held opposition to same-sex marriage.

"There is no putting this genie back in the bottle. It is undeniable. The shift is here and we're not going back," Republican strategist and CNN contributor Ana Navarro said Sunday.

One prominent Republican, Sen. Rob Portman of Ohio, endorsed that shift this month, two years after his son revealed to him that he is gay.

The case being heard Tuesday is Hollingsworth v. Perry (12-144), dealing with Proposition 8. And coming up Wednesday is U.S. v. Windsor (12-307), which deals with the DOMA issue.